Pieces
Each side has 8 pieces representing different animals, each with a different rank. Higher ranking pieces can capture all pieces of identical or weaker ranking. However, there is one exception: The elephant may not capture the mouse while the mouse may capture the elephant. The animal ranking, from strongest to weakest, is:

Movement
Players alternate moves with White moving first. During their turn, a player must move. Each piece moves one square horizontally or vertically (not diagonally). A piece may not move to its own den.

There are special rules related to the water squares:

The Mouse is the only animal that is allowed to go onto a water square.
The Mouse may not capture the Elephant or another Mouse on land directly from a water square.
The Mouse may attack the opponent Mouse in the water if both pieces are in the water.
A Mouse on land may not attack a mouse in the water.
The Lion and Tiger pieces may jump over a river by moving horizontally or vertically. They move from a square on one edge of the river to the next non-water square on the other side. Such a move is not allowed if there is a Mouse (whether or not friendly or enemy) on any of the intervening water squares. The Lion and Tiger are allowed to capture enemy pieces by such jumping moves.

Capturing
Animals capture the opponent pieces by "eating" them. A piece can capture any enemy piece which has the same or lower rank, with the following exceptions:

The Mouse may kill (capture) the Elephant. Many published versions of the game say this is done by the Mouse crawling in the Elephant's ear and gnawing at his brains. As stated above, the Mouse may not capture the Elephant from a water square. The powers of the Mouse resemble those of the Spy in Stratego.
The player may capture any enemy piece in one of the player's trap squares regardless of rank.

Variations
There are some commonly played variations to the rules official published by the board/pieces maker as follows:

The Elephant may not kill the Mouse under any circumstances. This is because a mouse is able to dodge the attack of an elephant because of its size.
The Leopard may jump over the river horizontally but not vertically (due to its lesser strength than the Tiger or Lion). It cannot jump over a mouse in the river though.
All traps are universal. If an animal goes into a trap in its own region, an opponent animal is able to capture it regardless of rank difference if it is beside the trapped animal. The rules for being on one's own trap do vary.
Some play the Wolf to be stronger than the Dog.
The rules for the Mouse to capture either the Elephant or Mouse from or into the water do vary.
There is a simplified version called Animal Checkers, which has no traps or rivers, and only the Mouse, Dog, Tiger and Elephant. [2]
Amongst the many examples shown on gameboardgeek there is at least one where the pieces are designed so that they are no longer visible by the opponent (mounted as a card on a stand like Stratego pieces). This apparently minor change alters the game from one of stochastic 'full-knowledge' to one of partial-knowledge.
There is a version of the game that limits which animals (levels 1 - 4) can move on to the trap squares.

I went ahead and tried it. It's okay, but not great. The first time I played the background did not load, so the pieces were just on a black screen that was still governed by the rules of the regular playing field, it just wasn't visible, an app restart fixed the problem and hasn't happened again. The in game instructions didn't have anything to say about the traps, so I had to figure that by trial and error. I can't really see recommending it as it is currently to anyone aside from fans of the game looking for a portable release. I probably would have been disappointed had I paid for it even though it's only $0.99 as even on the highest difficulty setting, it isn't incredibly challenging and as such is only fulfilling the first time or two you win. There is an option for pass-and-play multiplayer, but I don't see myself using that at all.

A few things that are lacking:
No option to include numbers was annoying especially since I'm new to the game and toward the lower end of the food chain things with the dogs get a little fuzzy.
There only distinction between player tiles is the direction the animal is facing, I wouldn't have minded a color border or something, not a huge issue though.
More board variations would have been welcome even though it's probably not official, as it stands the only thing that you can change is the background skin.

For anyone that does decide to purchase, I tested some of the side rules mentioned above:
The Elephant may not kill the Mouse.
The Leopard may not jump over the river at all.
Traps are not universal. So creatures on friendly traps behave according to normal numeric rules.

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